Geometric-Arithmetic Master Equation in Large and Fast Open Quantum
Systems
- URL: http://arxiv.org/abs/2112.07863v2
- Date: Sun, 13 Nov 2022 00:12:51 GMT
- Title: Geometric-Arithmetic Master Equation in Large and Fast Open Quantum
Systems
- Authors: Dragomir Davidovic
- Abstract summary: Understanding nonsecular dynamics in open quantum systems is addressed here, with emphasis on systems with large numbers of Bohr frequencies, zero temperature, and fast driving.
We employ the master equation, which replaces arithmetic averages of the decay rates in the open system, with their geometric averages.
We find that it can improve the second order theory, known as the Redfield equation, while enforcing complete positivity on quantum dynamics.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Understanding nonsecular dynamics in open quantum systems is addressed here,
with emphasis on systems with large numbers of Bohr frequencies, zero
temperature, and fast driving. We employ the master equation, which replaces
arithmetic averages of the decay rates in the open system, with their geometric
averages, and find that it can improve the second order perturbation theory,
known as the Redfield equation, while enforcing complete positivity on quantum
dynamics. The characteristic frequency scale that governs the approximation is
the minimax frequency: the minimum of the maximum system oscillation frequency
and the bath relaxation rate; this needs to be larger than the dissipation rate
for it to be valid. The concepts are illustrated on the Heisenberg
ferromagnetic spin-chain model. To study the accuracy of the approximation, a
Hamiltonian is drawn from the Gaussian unitary ensemble, for which we calculate
the fourth order time convolutionless master equation, in the Ohmic bath at
zero temperature. Enforcing the geometric average, decreases the trace distance
to the exact solution. Dynamical decoupling of a qubit is examined by applying
the Redfield and the geometric-arithmetic master equations, in the interaction
picture of the time dependent system Hamiltonian, and the results are compared
to the exact path integral solution. The geometric-arithmetic approach is
significantly simpler and can be super-exponentially faster compared to the
Redfield approach.
Related papers
- Markovian and non-Markovian master equations versus an exactly solvable model of a qubit in a cavity [0.0]
Quantum master equations are commonly used to model the dynamics of open quantum systems, but their accuracy is rarely compared with the analytical solution of exactly solvable models.
We consider the non-Markovian time-conless master equation up to the second (Redfield) and fourth orders as well as three types of Markovian master equations.
We demonstrate that the coarse-grained master equation outperforms the standard RWA-based Lindblad master equation for weak coupling or high qubit frequency.
arXiv Detail & Related papers (2024-03-15T01:06:06Z) - Invalidation of the Bloch-Redfield Equation in Sub-Ohmic Regime via a Practical Time-Convolutionless Fourth-Order Master Equation [0.0]
We optimize the computation of the fourth-order time-convolutionless master equation to meet this need.
Our master equation accounts for simultaneous relaxation and dephasing, resulting in coefficients proportional to the system's spectral density over frequency derivative.
We analyze the approach to a ground state in a generic open quantum system and demonstrate that it is not reliably computed by the Bloch-Redfield equation alone.
arXiv Detail & Related papers (2023-10-23T16:51:25Z) - GRAPE optimization for open quantum systems with time-dependent
decoherence rates driven by coherent and incoherent controls [77.34726150561087]
The GRadient Ascent Pulse Engineering (GRAPE) method is widely used for optimization in quantum control.
We adopt GRAPE method for optimizing objective functionals for open quantum systems driven by both coherent and incoherent controls.
The efficiency of the algorithm is demonstrated through numerical simulations for the state-to-state transition problem.
arXiv Detail & Related papers (2023-07-17T13:37:18Z) - Free expansion of a Gaussian wavepacket using operator manipulations [77.34726150561087]
The free expansion of a Gaussian wavepacket is a problem commonly discussed in undergraduate quantum classes.
We provide an alternative way to calculate the free expansion by recognizing that the Gaussian wavepacket can be thought of as the ground state of a harmonic oscillator.
As quantum instruction evolves to include more quantum information science applications, reworking this well known problem using a squeezing formalism will help students develop intuition for how squeezed states are used in quantum sensing.
arXiv Detail & Related papers (2023-04-28T19:20:52Z) - Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent
and Incoherent Photons Found with Gradient Search [77.34726150561087]
We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control.
We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
arXiv Detail & Related papers (2023-02-28T07:36:02Z) - Simulating Markovian open quantum systems using higher-order series
expansion [1.713291434132985]
We present an efficient quantum algorithm for simulating the dynamics of Markovian open quantum systems.
Our algorithm is conceptually cleaner, and it only uses simple quantum primitives without compressed encoding.
arXiv Detail & Related papers (2022-12-05T06:02:50Z) - Canonically consistent quantum master equation [68.8204255655161]
We put forth a new class of quantum master equations that correctly reproduce the state of an open quantum system beyond the infinitesimally weak system-bath coupling limit.
Our method is based on incorporating the knowledge of the reduced steady state into its dynamics.
arXiv Detail & Related papers (2022-05-25T15:22:52Z) - On optimization of coherent and incoherent controls for two-level
quantum systems [77.34726150561087]
This article considers some control problems for closed and open two-level quantum systems.
The closed system's dynamics is governed by the Schr"odinger equation with coherent control.
The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
arXiv Detail & Related papers (2022-05-05T09:08:03Z) - Fast and differentiable simulation of driven quantum systems [58.720142291102135]
We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods.
We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
arXiv Detail & Related papers (2020-12-16T21:43:38Z) - Floquet theory for temporal correlations and spectra in time-periodic
open quantum systems: Application to squeezed parametric oscillation beyond
the rotating-wave approximation [0.0]
We propose a method to compute two-time correlations and corresponding spectral densities of time-periodic open quantum systems.
We show how the quantum Langevin equations for the fluctuations can be efficiently integrated by partitioning the time domain into one-period duration intervals.
arXiv Detail & Related papers (2020-05-17T13:25:04Z) - Completely Positive, Simple, and Possibly Highly Accurate Approximation
of the Redfield Equation [0.0]
This approximation only truncates terms in the Redfield equation that average out over a time-scale typical of the quantum system.
GAME (geometric-arithmetic adaptable master equation) is between its time-independent, time-dependent, and Floquet form.
In the solvable exactly, three-level, Jaynes-Cummings model, we find that the error of the approximate state is almost an order of magnitude lower than that obtained by solving the coarse-grained master equation.
arXiv Detail & Related papers (2020-03-20T01:23:37Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.